Maximum number of minimum dominating and minimum total dominating sets (Q2878219)
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scientific article; zbMATH DE number 6335657
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maximum number of minimum dominating and minimum total dominating sets |
scientific article; zbMATH DE number 6335657 |
Statements
28 August 2014
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domination number
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total domination number
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extremal graphs
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math.CO
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0.96312094
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0.9607978
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0.9395069
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0.93885064
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0.91953677
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Maximum number of minimum dominating and minimum total dominating sets (English)
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Given a connected graph of order \(n\) and domination or total domination number \(\gamma\), the paper considers the problem of determining the maximum number of minimum (total) dominating sets. The problem is solved for \(\gamma = 2\) for the domination number and for the total domination number. For larger \(\gamma\), a construction is given that yields a non-trivial lower bound for the domination number.
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